Weighted L_p-norm inequalities in convolutions and their applications

Nhan, Nguyen Du Vi; Duc, Dinh Thanh

doi:10.7153/jmi-02-06

Cited by 15 publications

(4 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Next, in a series of papers [13][14][15][16][17] (see also [18][19][20][21]), Nhan et al considered a different generalization of the standard convolution, denoted by * ϕ , defined by…”

Section: Introductionmentioning

confidence: 99%

On fractional convolutions and distributions

Jain

Kumar

2015

Integral Transforms and Special Functions

View full text Add to dashboard Cite

The present paper focuses on three types of fractional convolutions. First consideration is to extend the famous Young's inequality in the context of fractional convolution. Then for these convolutions, weighted iterated L p − L q inequalities have been investigated. Finally, the notion of fractional convolutions between functions and distributions and also between distributions has been defined and various corresponding properties have been studied.

show abstract

“…Next, in a series of papers [13][14][15][16][17] (see also [18][19][20][21]), Nhan et al considered a different generalization of the standard convolution, denoted by * ϕ , defined by…”

Section: Introductionmentioning

confidence: 99%

On fractional convolutions and distributions

Jain

Kumar

2015

Integral Transforms and Special Functions

View full text Add to dashboard Cite

show abstract

“…For other convolutions and integral operators, while not being exhaustive, we refer the reader to [1,2,3,8,12,13,14,15,16,17,18,22,25,26,28]. In addition, it is relevant to have in mind that the factorization property of convolutions is crucial in solving corresponding convolution type equations [6,7,11,25].…”

Section: Introductionmentioning

confidence: 99%

New Convolutions for Quadratic-Phase Fourier Integral Operators and their Applications

2018

View full text Add to dashboard Cite

We obtain new convolutions for quadratic-phase Fourier integral operators (which include, as subcases, e.g., the fractional Fourier transform and the linear canonical transform). The structure of these convolutions is based on properties of the mentioned integral operators and takes profit of weight-functions associated with some amplitude and Gaussian functions. Therefore, the fundamental properties of that quadraticphase Fourier integral operators are also studied (including a Riemann-Lebesgue type lemma, invertibility results, a Plancherel type theorem and a Parseval type identity).As applications, we obtain new Young type inequalities, the asymptotic behaviour of some oscillatory integrals, and the solvability of convolution integral equations.

show abstract

“…Proposition 2.5 was expanded in various directions with applications to inverse problems and partial differential equations through L p (p > 1) versions and converse inequalities. See, for example, [6][7][8][19][20][21][22][23][24][25][26][27][28][29].…”

Section: Examplementioning

confidence: 99%

“…In particular, for the product of two Hilbert spaces, the idea gives generalizations of convolutions and the related natural convolution norm inequalities. These norm inequalities gave various generalizations and applications to forward and inverse problems for linear partial differential equations, see for example, [4,[6][7][8][19][20][21][22][23][24][25][26][27][28][29]. Furthermore, surprisingly enough, for some very general nonlinear systems, we can consider similar problems (see [26] for details).…”

mentioning

confidence: 99%